Mathematics · Permutations and Combinations

JEE Main 2025 — 22 January, Evening Shift — Question 2

In a group of 3 girls and 4 boys, there are two boys $B_{1}$ and $B_{2}$ . The number of ways, in which these girls and boys can stand in a queue such that all the girls stand together, all the boys stand together, but $\mathrm{B}_{1}$ and $\mathrm{B}_{2}$ are not adjacent to each other, is :

Option A:
144
Correct
Option B:
72
Option C:
96
Option D:
120

Answer: A

Step-by-step solution

Total - when $B_{1}$ and $B_{2}$ are together

$=2!(3!4!)-2!(3!(3!2!))=144$

Answer key and solution verified before publishing.

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Exam: JEE Main 2025
Paper: 22 January, Evening Shift
Subject: Mathematics
Chapter: Permutations and Combinations
Topic: Distribution of Objects into Groups